Abstract
Broadcast is the task of disseminating a message from any node to all the other nodes in a network. A minimal broadcast network (mbn) withn nodes is a communication network in which a message originated at any node can be broadcasted in [log2 n] time units. An optimal broadcast network (obn) is an mbn with minimum number of edges. No method is known for constructing an obn with an arbitrary number of nodes. In this paper, a new method called the doubling procedure is presented to construct mbn's with 2n and 2n?1 nodes when an obn or a good mbn withn nodes is known. The new construction method is based on the concepts of center node and center node set of an mbn. An algorithm is proposed to find a center node set of a given mbn. It is shown that an obn with 2n nodes can be constructed based on a known obn withn nodes for alln ≤ 9,n=15, 31 and 63,n=2 m ?1 andn=2 m ,m?Z +, by applying the doubling procedure. This method also generates the best mbn's for some values of [n≤64.
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